<p>For multivariate, single-step genomic best linear unbiased prediction analyses fitting a breeding value model, it is often assumed that the proportions of total genetic variance accounted for by genomic markers and residual polygenic effects are the same for all traits. Different covariance matrices for the two types of genetic effects are readily taken into account by fitting them separately. However, this can lead to slow convergence rates in iterative solution schemes. We propose an alternative computing strategy which – exploiting a canonical transformation – allows for trait-specific covariances whilst directly fitting total genetic effects only. Its effects on convergence rates and gains in accuracy and bias of genomic evaluation compared to analyses assuming proportionality of covariance matrices are examined using a small simulation study. Results show comparatively little improvement in accuracies but worthwhile reductions in overdispersion of predicted genetic merits for genotyped individuals without phenotypes.</p>